相关论文: Global weak solutions to a two-dimensional doubly …

We are concerned with the following doubly degenerate nutrient taxis system \begin{align} \begin{cases}\tag{$\star$}\label{eq-0.1} u_t=\nabla\cdot(u v\nabla u)-\nabla\cdot(u^{2} v\nabla v)+u-u^2,\\[1mm] v_t=\Delta v-u v, \end{cases}…

This paper is concerned with the doubly degenerate nutrient taxis system $u_t=\nabla \cdot(u^{l-1} v \nabla u)- \nabla \cdot\left(u^{l} v \nabla v\right)+ uv$ and $v_t=\Delta v-u v$ for some $l \geqslant 1$, subjected to homogeneous Neumann…

In this work, we study the no-flux initial-boundary value problem for the doubly degenerate nutrient taxis system \begin{align} \begin{cases}\tag{$\star$}\label{eq 0.1} u_t=\nabla \cdot(u v \nabla u)-\chi \nabla \cdot\left(u^{2} v \nabla…

The doubly degenerate nutrient taxis system \begin{equation}\label {0.1} \left\{ \begin{aligned} &u_{t}=\nabla \cdot (uv\nabla u)-\chi \nabla \cdot (u^{\alpha}v\nabla v)+\ell uv,&x\in \Omega,\, t>0,\\ & v_{t}=\Delta v-uv,&x\in \Omega,\,…

This work addresses the one-dimensional Cauchy problem for the doubly degenerate nutrient taxis model \begin{equation*} \begin{cases} \displaystyle \frac{\partial u}{\partial t} = \frac{\partial}{\partial x}(u v u_x) -…

This work studies the following doubly degenerate parabolic-elliptic nutrient taxis system $$ \begin{cases} u_t = (uvu_x)_x -(u^2 vv_x)_x + uv, \\[1.5 ex] \hspace{0.2 cm}0 = v_{xx} - uv + f(x,t), \end{cases} $$ in a bounded interval $\Omega…

Motivated by the study of bacteria's response to environmental conditions, we consider the doubly degenerate nutrient taxis system \begin{align*} \begin{cases} u_t=\nabla\cdot(uv\nabla u)-\chi\nabla\cdot(u^{\alpha}v\nabla v)+\ell uv,\\…

This work considers the doubly degenerate nutrient model \begin{equation*}\label{AH1} \left\{ \begin{split} &u_t=\nabla\cdot\left(u^{m-1}v\nabla u\right)-\nabla\cdot\left(f(u)v\nabla v\right)+\ell uv,&&x\in\Omega,\,t>0, &v_t=\Delta v-uv,…

We study a doubly tactic resource consumption model \bess \left\{\begin{array}{lll} u_t=\tr u-\nabla\cd(u\nabla w),\\[1mm] v_t=\tr v-\nabla\cd(v\nabla u)+v(1-v^{\beta-1}),\\[1mm] w_t=\tr w-(u+v)w-w+r \end{array}\right. \eess in a smooth…

This paper considers the degenerate and singular chemotaxis-Navier--Stokes system with logistic term $n_t + u\cdot\nabla n =\Delta n^m - \chi\nabla\cdot(n\nabla c) + \kappa n -\mu n^2$, $x \in \Omega,\ t>0$, $c_t + u\cdot\nabla c = \Delta c…

Systems of the type $$\begin{cases} u_t = \nabla \cdot (D_1(u) \nabla u - S_1(u) \nabla v) + f_1(u, v),\\ v_t = \nabla \cdot (D_2(v) \nabla v + S_2(v) \nabla u) + f_2(u, v) \end{cases} \qquad (\star)$$ can be used to model pursuit-evasion…

We prove existence of global weak solutions to the chemotaxis system $ u_t=\Delta u - \nabla\cdot (u\nabla v) +\kappa u -\mu u^2 $ $ v_t=\Delta v-v+u $ under homogeneous Neumann boundary conditions in a smooth bounded convex domain…

In this paper, we study a nutrient-taxis model with porous medium slow diffusion \begin{align*} \left\{ \begin{aligned} &u_t=\Delta u^m-\chi\nabla\cdot(u\nabla v)+\xi uv-\rho u, \\ &v_t-\Delta v=-vu+\mu v(1-v), \end{aligned}\right.…

We consider the potentially degenerate haptotaxis system \begin{equation*} \left\{ \begin{aligned} u_t &= \nabla \cdot (\mathbb{D} \nabla u + u \nabla \cdot \mathbb{D}) - \chi \nabla \cdot (u\mathbb{D}\nabla w) + \mu u(1-u^{r- 1}), \\ w_t…

In this paper we study the initial boundary value problem for the system\\ $-\mbox{{div}}\left[(I+\mathbf{m} \mathbf{m}^T)\nabla p\right]=s(x),\ \…

This paper deals with the oncolytic virotherapy model \begin{equation}\begin{split} \begin{cases} &u_t = \Delta u - \nabla \cdot (u\nabla v)-uz +\mu u(1-u),& \\[2ex] &v_t = - (u+w)v,& \\[2ex] &w_t = D_w \Delta w - w + uz,& \\[2ex] &z_t =…

The continuous dependence on the initial data and consequently the uniqueness of bounded weak solutions to a class of triangular reaction-cross-diffusion equations is shown. The class includes two-species doubly degenerate equations for…

We consider 1D dissipative transport equations with nonlocal velocity field: \[ \theta_t+u\theta_x+\delta u_{x} \theta+\Lambda^{\gamma}\theta=0, \quad u=\mathcal{N}(\theta), \] where $\mathcal{N}$ is a nonlocal operator given by a Fourier…

This paper deals with the Neumann boundary value problem for the system $$u_t=\nabla\cdot\left(D(u)\nabla u\right)-\nabla\cdot\left(S(u)\nabla v\right)+f(u) ,\quad x\in\Omega,\ t>0$$ $$v_t=\Delta v-v+u,\quad x\in\Omega,\ t>0$$ in a smooth…

This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system \begin{eqnarray*} \begin{array}{llc} u_t=\Delta u-\chi\nabla\cdot (u\nabla v)+\kappa u-\mu u^2,\\ v_t=\Delta v-uv, \end{array}…